# Algebra

## 1811 Submissions

[6] **viXra:1811.0441 [pdf]**
*submitted on 2018-11-27 21:36:42*

### An Insight into Higher Order Logic (HOL) based Ontology NeuroInformatics Framework by Considering Ontology Oriented Concepts & Language/s based on HOL/Grobner Bases/Scala/Jikes RVM/JVMTechnologies/IoT Computing Environments.

**Authors:** Nirmal Tej Kumar

**Comments:** 7 Pages. Short Communication & Technical Notes

“Gröbner Bases Theory” & Ontology could be implemented as explained - An Insight into Higher Order Logic (HOL) based Ontology Neuroinformatics Framework by Considering Ontology Oriented Concepts & Language/s based on HOL/Grobner Bases/Scala/Jikes RVM/JVM Technologies/IoT Computing Environments.

**Category:** Algebra

[5] **viXra:1811.0370 [pdf]**
*submitted on 2018-11-24 01:52:02*

### Factorization Of Sum Of Squares Of Two Real Numbers

**Authors:** Tushar Bhausaheb Kadus

**Comments:** 6 Pages.

In Mathematics factorization of sum of squares of two real numbers is often needed. But
there was no formula to do that. Hence I have proposed a new formula : Let a and b be two
real numbers then the sum of their squares, that is a²+b² is equal to a(a+b)−b(a−b). In this
paper, we prove and examine the proposed formula.

**Category:** Algebra

[4] **viXra:1811.0310 [pdf]**
*replaced on 2018-11-25 06:15:59*

### A General Definition of Division in a Field

**Authors:** Hiroshi Okumura

**Comments:** 2 Pages.

The historical definition of division by zero given by Brahmagupta is correct.

**Category:** Algebra

[3] **viXra:1811.0283 [pdf]**
*submitted on 2018-11-18 20:46:54*

### To Divide by Zero is to Multiply by Zero

**Authors:** Hiroshi Okumura

**Comments:** 1 Page.

A remark of the definition of division by zero is given.

**Category:** Algebra

[2] **viXra:1811.0236 [pdf]**
*submitted on 2018-11-15 19:52:46*

### Splitting of Quasi-Definite Linear System Maintains Inertia

**Authors:** Martin Neuenhofen

**Comments:** 4 Pages.

We show that there is a variety of Schur complements that yield a decoupling of a quasi-definite linear system into two quasi-definite linear systems of half the size each. Splitting of linear systems of equations via Schur complements is widely used to reduce the size of a linear system of equations. Quasi-definite linear systems arise in a variety of computational engineering applications.

**Category:** Algebra

[1] **viXra:1811.0144 [pdf]**
*submitted on 2018-11-10 00:56:54*

### The Importance of Quaternions & Rotational Systems in the Context of Cryo-EM Image Processing – A Simple Suggestion On Using HOL/JVM/JikesRVM/Image J Based Computing Environments.

**Authors:** Nirmal Tej Kumar

**Comments:** 3 Pages. Short Communication & Technical Notes

As the title suggests it is our sincere desire to explore “Quaternions & Rotational Systems” in the highly promising domains of Cryo-EM Image Processing to probe the frontiers of Nano-Bio Systems.

**Category:** Algebra